Question

the three angles of given triangle are in ratio 1:2:1.Find all angles of the triangle.classify the triangle into 2 different ways

Answer 1

GiveN :-

• The three angles of a triangle are in ratio 1:2:1 .

To FinD :-

• The all angles of the triangle.
• Classify the triangle on two basis.

SolutioN :-

Let us take the given ratio be 1x : 2x : 1x .

Now , we know that the angle sum property of a triangle is 180° . So ,

According to the Question ;

⇒ 1x + 2x + 1x = 180°

⇒ 4x = 180°

⇒ x = 180°/4 .

⇒ x = 45°

Hence ,

• First angle = 1x = 45°
• Second angle = 2x = 90°
• Third angle = 1x = 45°

$\Large\boxed{\pink{\sf Angles :-45^{\circ}\:,90^{\circ}\:,45^{\circ}}}$

Classification of the triangle :-

1) Firstly we can classify the triangle on the basis of its angle. Here we can see that one angle of the triangle is 90° . So , the triangle is a right angle triangle

2) thirdly we can classify the triangle on the basis of its side. Here two angles are 45° . and we know sidea opposite to equal angles are equal.

Hence the two sides are equal . Hence the triangle is a Isosceles triangle .

$\Large\boxed{\purple{\sf Classification-Isosceles \:\&\:Right\;\triangle}}$